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Solving boundary value problems on manifolds with a plane waves method

2020-09Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorAlves, Carlos J. S.
dc.contributor.authorAntunes, Pedro R. S.
dc.contributor.authorMartins, Nuno F. M.
dc.contributor.authorValtchev, Svilen S.
dc.date.accessioned2025-09-16T17:32:14Z
dc.date.available2025-09-16T17:32:14Z
dc.date.issued2020-09
dc.description.abstractIn this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial differential equations on manifolds. In particular, the method is applied to the Helmholtz–Beltrami equations. We prove density results that justify the completeness of the plane waves space and justify the approximation of domain and boundary data. A-posteriori error estimates and numerical experiments show that this simple technique may be used to accurately solve boundary value problems on manifolds.eng
dc.description.sponsorshipThe financial support of the Portuguese Fundação para a Ciência e a Tecnologia (FCT), through the projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/IST-ID (first, third and fourth author) and PTDC/MAT-CAL/4334/2014 (second author), is gratefully acknowledged.
dc.identifier.citationCarlos J.S. Alves, Pedro R.S. Antunes, Nuno F.M. Martins, Svilen S. Valtchev, Solving boundary value problems on manifolds with a plane waves method, Applied Mathematics Letters, Volume 107, 2020, 106426, ISSN 0893-9659, https://doi.org/10.1016/j.aml.2020.106426.
dc.identifier.doi10.1016/j.aml.2020.106426
dc.identifier.issn0893-9659
dc.identifier.urihttp://hdl.handle.net/10400.8/14079
dc.language.isoeng
dc.peerreviewedyes
dc.publisherElsevier
dc.relationCenter for Computational and Stochastic Mathematics
dc.relation.hasversionhttps://www.sciencedirect.com/science/article/pii/S0893965920301919?via%3Dihub
dc.relation.ispartofApplied Mathematics Letters
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectMeshfree method
dc.subjectPlane waves method
dc.subjectHelmholtz–Beltrami operator
dc.subjectManifolds
dc.titleSolving boundary value problems on manifolds with a plane waves methodeng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Computational and Stochastic Mathematics
oaire.awardURIhttp://hdl.handle.net/10400.8/13612
oaire.citation.endPage8
oaire.citation.startPage1
oaire.citation.titleApplied Mathematics Letters
oaire.citation.volume107
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameValtchev
person.givenNameSvilen
person.identifier.ciencia-idAF1E-BD9D-A8D7
person.identifier.gsidhttps://scholar.google.com/citations?user=MtxwhiUAAAAJ&hl=en
person.identifier.orcid0000-0002-3474-2788
person.identifier.scopus-author-id8361079200
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In this paper we consider a plane waves method as a numerical technique for solving boundary value problems for linear partial differential equations on manifolds. In particular, the method is applied to the Helmholtz–Beltrami equations. We prove density results that justify the completeness of the plane waves space and justify the approximation of domain and boundary data. A-posteriori error estimates and numerical experiments show that this simple technique may be used to accurately solve boundary value problems on manifolds.
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